Interferometers are often preferred over probe-based coordinate measuring machines for measuring test surfaces because the interferometers measure the entire test surfaces at once whereas the coordinate measuring machines measure the test surfaces one point at a time. Movements of the coordinate measuring machines between the different measuring points detract from the accuracy of the measures and require a more controlled operating environment to minimize changes in the test surface during the extended period of measurement.
Interferometers produce images of surfaces in the form of interference patterns that represent contour maps of surface variations. The interference pattern is created by combining a test wavefront (or beam) reflected from the test surface with a reference wavefront (or beam) representing a theoretical reflection from the surface. The two wavefronts are shaped by reflective or refractive optics. Highly reflective surfaces are usually measured by arranging the test wavefront to strike the test surface at normal incidence. Surfaces having lower reflectance are measured at grazing incidence.
However, interferometers are seldom used to measure surfaces other than planes or spheres because matching wavefronts are difficult to produce. Anamorphic optical elements can be used to produce the matching wavefronts; but these elements are expensive, difficult to make and test, and limited in accuracy. More conventional optics can also be used to construct the matching wavefronts by combining smaller portions of spherical or nearly spherical wavefronts. However, combining multiple measurements of conventional optics is time consuming and may require instrument motions that also detract from accuracy.
A less well-known and little developed interferometric approach to measuring both planar and cylindrical surfaces involves the use of diffractive optics for relatively shaping test and reference wavefronts. For example, a 1973 paper entitled "Oblique Incidence Interferometry Applied to Non-Optical Surfaces" by K. G. Birch, Journal of Physics E: Scientific Instruments, Volume 6, reports on the use of a pair of identical diffraction gratings for measuring planar surfaces at grazing incidence. The first diffraction grating divides test and reference wavefronts into different diffraction orders. The test wavefront is reflected from a planar test surface and is recombined with the reference wavefront at the second diffraction grating.
East German Patent 106769 issued to Johannes Schwider in 1974 proposes use of two identical gratings for measuring cylindrical surfaces at grazing incidence. The first diffraction grating divides a planar primary wavefront into test and reference wavefronts. The test wavefront is diffracted into an axiconic wavefront that is reflected from a cylindrical test surface at grazing incidence. The reference wavefront is transmitted without change. The second diffraction grating recombines the two wavefronts by transmitting the test wavefront without further change and by diffracting the reference wavefront into the axiconic shape of the test wavefront.
Little practical exploitation of these ideas has been achieved over the last 20 years. Many other alternatives are available for measuring planar surfaces; and further developments are required to provide accurate measurements over a wider range of surface geometries, especially test surfaces that further affect the shape of the test wavefront. Practical considerations relating to alternative setups for particular test pieces, efficiency of light conveyance, and control over image contrast remain unresolved.